PreprintarXiv licencearXiv
Simultaneous non-vanishing of twists of GL3 and GL1 L-functions
Abstract
We show that for a fixed SL3(ℤ) Hecke--Maass cusp form F, there are infinitely many primitive Dirichlet characters χ such that L(1/2, F× χ) and $L(1/2, χ)$ do not vanish \emph{simultaneously}. More precisely, we obtain an asympotic formula with a {\em power-saving} error term for the product of these central values averaged over {χbmod q: q∈ 𝒬} where 𝒬 is a set of squarefree integers with a small divisor of suitable size.
Related
- Uniform non-vanishing of prime quadratic twists of standard and symmetric square L-functions
- Simultaneous nonvanishing of quadratic twists via Rankin-Cohen brackets
- Nonvanishing of 2-primary Kolyvagin classes via simultaneous quadratic twists
- Iwasawa invariants of sharp/flat $2$-adic L-functions for quadratic twists of elliptic curves
- Central non-vanishing of Dirichlet L-functions
BibTeX
@misc{li2026simultaneous,
title = {{Simultaneous non-vanishing of twists of $\mathrmGL_3$ and $\mathrmGL_1$ $L$-functions}},
author = {Junxian Li and Xiannan Li and Yongxiao Lin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10661},
eprint = {2610.10661},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10661},
}
RIS
TY - UNPB
TI - Simultaneous non-vanishing of twists of GL_3 and GL_1 L-functions
AU - Junxian Li
AU - Xiannan Li
AU - Yongxiao Lin
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10661
UR - https://arxiv.org/abs/2610.10661
AB - We show that for a fixed SL_3(ℤ) Hecke--Maass cusp form F, there are infinitely many primitive Dirichlet characters χ such that L(1/2, F× χ) and $L(1/2, χ)$ do not vanish \emph{simultaneously}. More precisely, we obtain an asympotic formula with a {\em power-saving} error term for the product of these central values averaged over {χbmod q: q∈ 𝒬} where 𝒬 is a set of squarefree integers with a small divisor of suitable size.
ER -